1. Field of the Invention
The present invention relates generally to turbine rotor blades and, more particularly, to turbine rotor blade rows having blades with two alternating resonant frequencies and a method for preventing unstalled flutter employing the same.
A steam turbine rotor has several rows of rotor blades. Although rotor blades typically share the same general shape, that is, each typically has a base portion and an airfoil portion including a leading edge, a trailing edge, a concave surface, and a convex surface, the airfoil shape common to a particular row of rotor blades differs from the airfoil shape for every other row within that turbine. Likewise, no two turbines of different designs share the same airfoil shape. The structural differences in airfoil shape, which may appear minute to the untrained observer, result in significant variations in aerodynamic characteristics, stress patterns, operating temperature, and natural frequency of the airfoil. In the process of designing and fabricating rotor blades, it is critically important to tune the resonant frequency of the blades to minimize forced vibration. Blade tuning for steam turbines powered by fossil fuels first requires a determination of the harmonics of running speed. In a typical fossil steam turbine, the rotor rotates at 3,600 revolutions per minute (r.p.m.), or 60 cycles per second (c.p.s.). Since 1 c.p.s.=1 hertz (Hz), and since simple harmonic motion can be described in terms of the angular frequency of circular motion, the running speed of 60 c.p.s. produces a first harmonic of 60 Hz, a second harmonic of 120 Hz, a third harmonic of 180 Hz, a fourth harmonic of 240 Hz, etc. The harmonic series represents the characteristic frequencies of the normal modes of vibration of an exciting force acting upon the rotor blades. If the rotor blade natural frequencies of oscillation coincide with the frequencies of the harmonic series, or harmonics of running speed, a destructive resonance can result. It is standard practice in the art to tune the natural resonant frequencies of the rotor blades of a blade row to a frequency at a midpoint between two successive harmonics, such as 210 Hz, which is midway between the third and fourth harmonics. In a nuclear powered steam turbine, operating speed is 1800 r.p.m. Therefore, successive harmonics would be at 30 Hz, 60 Hz, 90 Hz, etc. Combustion turbines also experience flutter, and must be similarly tuned to avoid dangerous frequencies.
Selection of the two successive harmonics between which the blades are tuned depends on the particular blade. For example, some blades may have a naturally higher or lower frequency due to the length, shape, or some other parameter. While it is most desirable to have the natural resonant frequency of the blades fall exactly between two harmonics, it may be difficult to achieve a midway frequency given the other design parameters of the blade. In other words, there may be limits to the amount by which a practitioner can raise or lower the frequency of a blade without adversely affecting performance.
When all of the rotor blades of a row have the same natural resonant frequency, and when that frequency is at or near the midpoint between two successive harmonics of running speed, the effects of forced vibration are minimized. Forced vibration is generated by disturbances in the steam flow, and the frequency is expressed as the harmonics of running speed. It is standard practice to tune an entire row of blades to the same natural resonant frequency which is as close as possible to the midpoint of two harmonics of running speed.
In contrast to forced vibration, an aerodynamic phenomenon known as unstalled flutter may occur even if the blades are tuned properly between two harmonics of running speed. Unstalled flutter is a self excitation of the blades which may occur when blades having the same natural resonant frequency vibrate at a frequency close to their natural resonant frequency for the first mode of vibration. A "mode" of vibration refers to a direction of vibration, given that a blade can vibrate in a plurality of directions. The first mode of vibration is that which occurs predominantly in the direction of rotation of the blade. A blade will have a natural resonant frequency for each mode of vibration. Unstalled flutter occurs when two or more adjacent blades of a row move relative to each other in a certain phase relationship and vibrate at a frequency close to their natural frequency for the first mode.
Unstalled flutter is a problem which confronts a variety of types of rotor blades for fossil and nuclear steam turbines and combustion turbines. The occurrence of unstalled flutter places an unacceptable stress on the blades which may lead to blade failure. In a steam turbine, the last three stages of a low pressure steam turbine are believed to be more susceptible to flutter since these blades are "free standing". Lashing blades together tends to militate against unstalled flutter since it is less likely that blades will move relative to each other.
A need exists for an effective Way of preventing the occurrence of unstalled flutter for free standing turbine rotor blades.